The present invention addresses the problem of identifying an enemy target by considering a signal containing high levels of noise. FIG. 1 illustrates generally the problem of target detection. A signal 100 is received by an operator, the signal 100 may contain information about a target and the signal may be encumbered by high levels of noise. Ideally, a target detection device 102 is designed to extract target information from the signal and communicate to the operator 103 that a target is or is not present.
An operator will select a target detection device based on the probability of accurate detection by the device and also, in the case of multiple targets, the probability of target differentiation by the device. In military applications, detection of multiple targets is a critical problem because it is necessary to clearly distinguish friendly objects from hostile threats.
FIG. 2 illustrates a prior art common type of target detector, which is based on linear system dynamics. In FIG. 2, the signal S(t) 200 represents the target signal (consisting of one or the sum of multiple sine waves) which is to be detected. The noise 201 added in the input data is modeled via a noise source η(t) which sums with S(t) at the left side of the target detection block at 202. The linear system processes these data and has an output (variable x) 203. In the variable x, 203, the ratio of the power in the signal of the target S(t) to the noise η(t) may be expressed in terms of a signal to noise ratio of the following form as it appears in the output signal:S/N=Signal to Noise Ratio=(Power in S(t))/(Power in η(t))  (Eq. 1)
The present invention differs from the known prior art target detection devices in many significant aspects. In the present invention a “class” of nonlinear filters are defined in a mathematical sense that have not been previously known or published in the prior art. It will be shown that there exists an infinite number of possible SR filters that can be synthesized and a general mathematical expression of this “class” of filters will be discussed using potential energy and force methods. Further, all prior applications of the SR principle have dealt with the case that the signal to be identified is slightly less than a threshold value. This means the signal to noise ratio is approximately 1.0. This patent application deals with the case that the S/N ratio may be in the range of 1/10,000 or smaller.
From a practical standpoint, the present invention deals with target detection and not a communications system application. The approach here is to use the Fourier series decomposition of the target signal to state the claim of improved target identification. This clearly distinguishes the present invention from the prior art. Further, none of the prior art has shown a specific procedure on how to relate the noise level to specific parameters in the filter design. Finally, the present invention discloses unique data on how the amplification of S/N can be obtained using the techniques herein. The data demonstrate the efficacy of the proposed methods using extraordinarily high levels of noise to signal (greater than 10,000). Few known prior art systems have laboratory data to support the efficacy of their proposed methods.
For optimal target detection, the goal of the present invention is to make the ratio S/N as large as possible. If the S/N ratio is increasing, this improves the quality of the information we gather and enhances our ability to make good decisions. It should be noted that for strictly linear systems, such as that shown in FIG. 2, it is known that increasing the power in the noise η(t) can only degrade the S/N ratio and hence the ability of the linear detector to discern a target.